Question

A change machine changes dollar bills into quarters and nickels. lf you receive 12 coins after inserting a dollar bill, how many nickels did you receive?

Answer 1

`10`

Explanation:

If we write `n` for the number of nickels (5c) and `q` for the number of quarters (25c), then we have two simultaneous equations:

`100 = 25q+5n`

`12 = q+n`

Dividing both sides of the first equation by `5` we get:

`20 = 5q+n`

Multiplying both sides of the second equation by `5` we get:

`60 = 5q+5n`

Subtracting the previous equation, we find:

`40 = 4n`

Dividing both sides by `4` and transposing, we find:

`n = 10`

So there were `10` nickels, making `50`c and `2` quarters, making the other `50`c.